The effect of memory on moving average processes: Functional large deviations, long strange segments and ruin probabilities

Souvik Ghosh, Ph.D. Candidate

School of Operations Research and Information Engineering, Cornell University

January 22, 2008

4:00 P.M.; 223 Weber

ABSTRACT

The large deviations of an infinite moving average process with
exponentially light tails are very similar to those of an
i.i.d. sequence as long as the coefficients decay fast enough. If they
do not, the large deviations change dramatically. We study this
phenomenon in the context of functional large, moderate and huge
deviation principles. Then we look at its applications to long strange segments and ruin probabilities.